ON /-EXTREMALLY DISCONNECTED SPACES

Year 2007, Volume: 56 Issue: 1, 33 - 40, 01.02.2007

Aynur Keskin Şaziye Yüksel Takashi Noırı

https://doi.org/10.1501/Commua1_0000000195

Abstract

Abstract. We have introduced and investigated the notion of I-extremal disconnectedness on ideal topological spaces. First, we found that the notions of
extremal disconnectedness and I-extremal disconnectedness are independent
of each other. About the letter one, we observed that every open subset of
an I-extremally disconnected space is also an I-extremally disconnected space.
And also, in extremally disconnectedness spaces we have shown that I-open
set is equivalent almost I-open and every -I-open set is preopen. Finally,
we have shown that B-I-continuity( resp. pre-I-continuity, I-continuity ) is
equivalent to semi-I-continuity( resp. strongly -I-continuity, almost strongly
I-continuity ) if the domain is I-exteremally disconnected

Keywords

W eak regular-I-closed sets, I-open sets, I-extremally disconnectedspaces, topological ideal

References

• M. E. Abd El-Monsef, E. F. Lashien and A. A. Nasef, On I-open sets and I-continuous functions, Kyungpook Math. J. , 32(1) (1992), 21-30.
• M. E. Abd El-Monsef, R. A. Mahmoud and A. A. Nasef, Almost I-openness and almost I-continuity, J. Egypt. Math. Soc. ,7(2)(1999), 191-200.
• J. Dontchev, On Hausdorğ spaces via topological ideals and I-irresolute functions, Annals of the New York Academy of Sciences, Papers on General Topology and Applications, Vol. 767 (1995), 28-38.
• J. Dontchev, On pre-I-open sets and a decomposition of I-continuity, Banyan Math. J., 2 (1996).
• J. Dontchev, M. Ganster and D. Rose, Ideal resolvability, Topology Appl., 93 (1999), 1-16.
• J. Dontchev, M. Ganster and T. Noiri, Uni…ed operation approach of generalized closed sets via topological ideals, Math. Japon., 49 (1999), 395-401.
• E. Hatir and T. Noiri, On decomposition of continuity via idealization, Acta Math. Hungar., 96 (4)(2002) , 341-349.
• E. Hatir, A. Keskin and T. Noiri, On a new decomposition of continuity via idealization, JP J. Geometry&Topology, 1(3)(2003), 53-64.
• E. Hayashi, Topologies de…ned by local properties, Math. Ann., 156 (1964), 205-215.
• D. Jankovi´c and T. R. Hamlett, New topologies from old via ideals, Amer. Math. Monthly, 97 (1990), 295-310.
• J. Kelley, General Topology, D. Van Nostrand Co. Inc., Princeton, New Jersey, 1955.
• K. Kuratowski, Topology, Vol.I, Academic Press, New York, 1966.
• A.S.Mashhour, M.E.Abd-El Monsef and S.N.El-Deep, On precontinuous and weak precon
• tinuous mappings, Proc. Math. Phys. Soc. Egypt, 53 (1982), 47-53.
• Current address : Aynur KESKIN,Selcuk University, Department of Mathematics, 42075 Campus
• Konya TURKEY, Sazıye YUKSEL, Selcuk University, Department of Mathematics, 42031 Campus
• Konya TURKEY, Takashi NOIRI,2949-1 Shiokita-cho, Hinagu Yatsushiro-shi, Kumamoto-ken 869-5142 JAPAN E-mail address : [e-mail], [e-mail], [e-mail]